Abstract
The present paper concerns the problem of determining the variations in the six orbital elements of a planetary body when one or more of the original observations are affected by known errors. Differential expressions are derived for these variations which eliminate the necessity of having to re-compute the orbit several times. A numerical example is included in which results of these expressions are compared with actual residuals as obtained from two orbital calculations of the same asteroid.
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References
Heinrich K. Eichhorn,Mitteilungen der Universitäts-Sternwarte Wien, 5, 169–184 (1952).
In the case of the earth satellite, the observer is moving along a circle of latitude whose plane, unlike that of the satellite orbit, does not, necessarily, pass through the geocenter; whereas in the other case, both earth and planet are moving in Keplerian ellipses.
Heinrich K. Eichhorn,Mitteilungen der Universitäts-Sternwarte Wien, 4, 149–171 (1950).
Since a, e,and t o are related to the eccentric anomaly, E,by a transcendental equation, we follow the suggestion of Eichhorn and avoid considerable complication by first solving for the three eccentric anomalies corresponding to the three observation times, and then computing the changes in a, e,and t o from these intermediary elements.
The NAREC, built and operated by the Naval Research Laboratory, is a digital computer with a high-speed electrostatic storage system capable of retaining 1024 forty-f ive binary digit quantities and a slower magnetic drum holding 8192 such quantities. The time of access from these memory locations is 10 microseconds and 1/30 of a second, respectively, and the rate of mathematical calculations is about 11 000 operations per second, with a maximum accuracy of 13 decimal places. Auxiliary equipment provides for the preparation of tapes, the transcribing of information, and the plotting of results. Typical computations suitable for the NAREC include the solution of ordinary and partial differential equations, integral and simultaneous linear equations, the reduction of experimental data, and various problems of a logical nature.
The choice as to whether or not these simplifications should be included will, of course, depend entirely on the accuracy required of each particular application of this problem.
Kenneth P. Williams,The Calculation of the Orbits of Asteroids and Comets, The Principia Press, Inc., 153–167 (1934).
This system obtains the angular position of a radio source by measuring the difference in the radio path lengths from the source to each of two antennas. This difference is determined by means of a phase difference between the signal received at the antennas and at the receiver output.
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© 1961 Springer-Verlag Wien
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Weirauch, R.F. (1961). On the Accuracy of an Elliptical Orbit Determination. In: Reuterswärd, C.W.P. (eds) XIth International Astronautical Congress Stockholm 1960 / XI. Internationaler Astronautischer Kongress / XIe Congrès International D’Astronautique. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8071-6_38
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DOI: https://doi.org/10.1007/978-3-7091-8071-6_38
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-8073-0
Online ISBN: 978-3-7091-8071-6
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